Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C25 |
| direct product | C5×D7×#41 |
| Fitting | C5×C7×#41 ⋊ C2 |
| Hall | C5×C7 ⋊ C2×#41 |
| Sylow | C7 ⋊ C2×C5×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C5 | C22×D7 |
| commutator, cosocle | C2×C7 | C24×C5 |
| Frattini | C2 | C23×C5×D7 |
| Fitting | C5×C7×#41 | C2 |
| socle | C2×C5×C7 | C24 |
| hypercenter | C5×#41 | D7 |
| hypocenter | C7 | C2×C5×#41 |
| LCS | G ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C4×C5 ◁ C5×#41 | |
328 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 174 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 280 |
250 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#41×AGL(1,𝔽7), D5×D7×#41, C5×D7×AGL(1,ℤ/8), … |
| maximal normal subgroup of | C5×#41×AGL(1,𝔽7), D5×D7×#41, C5×D7×AGL(1,ℤ/8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 1037);